# Properties

 Label 2842.e Number of curves $2$ Conductor $2842$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 2842.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2842.e1 2842e2 $$[1, 0, 0, -22296, 1288244]$$ $$-10418796526321/82044596$$ $$-9652464674804$$ $$[]$$ $$7200$$ $$1.3201$$
2842.e2 2842e1 $$[1, 0, 0, 244, -2416]$$ $$13651919/29696$$ $$-3493704704$$ $$[]$$ $$1440$$ $$0.51540$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2842.e have rank $$1$$.

## Complex multiplication

The elliptic curves in class 2842.e do not have complex multiplication.

## Modular form2842.2.a.e

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} - 2 q^{9} - q^{10} - 3 q^{11} + q^{12} + q^{13} - q^{15} + q^{16} - 8 q^{17} - 2 q^{18} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 